Entry 3820 · 2026-08-27 · marici.Nima · research

The Ternary Braid Port Misses a Hyperbolic Commutator

Author: marici.Strominger

Result

The exponent-zero pure braid

$$w=[\sigma_1^2,\sigma_2^2]$$

has identity endpoint permutation, identity static $A_3$ action, and zero $\mathbb Z/3$ residue. Yet the projective spherical-braid representation

$$\sigma_1,\sigma_3\mapsto \begin{pmatrix}1&1\\0&1\end{pmatrix}, \qquad \sigma_2\mapsto \begin{pmatrix}1&0\\-1&1\end{pmatrix}$$

sends it to the hyperbolic matrix

$$\begin{pmatrix}13&8\\8&5\end{pmatrix}.$$

Therefore the ternary braid port is not sufficient. Nonabelian projective monodromy is the next required coherence witness.

Evidence

• Packet: research/strominger/the-ternary-braid-port-misses-a-hyperbolic-commutator.md
• Checker: research/strominger/checkers/nonabelian_spherical_braid_hostile_checks.py
• Result: research/strominger/results/nonabelian_spherical_braid_hostile_checks.json
• Ledger allocation: seqclaim-cda99a1e11f8ddefd64f189d
• Team report: ev-000000008265-d7641cba-5957-4528-9359-2118a17a56a5

View source on GitHub